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Heavy ion spectral breaks in large SEP events

LWS Team Meeting CIT, Pasadena, CA Jan 10 th -11 th , 2008. Heavy ion spectral breaks in large SEP events. Gang Li. Scenario check. Close to the sun, where the acceleration occurs …. Comaring shock scale with particle length scale.

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Heavy ion spectral breaks in large SEP events

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  1. LWS Team Meeting CIT, Pasadena, CA Jan 10th-11th , 2008 Heavy ion spectral breaks in large SEP events Gang Li

  2. Scenario check Close to the sun, where the acceleration occurs … Comaring shock scale with particle length scale. In a magnetic field, this length scale is given by Rg, the gyroradius. If acceleration is done by say, 30 minutes, and shock has a speed of 2000 km/s => r = 3.6 10^6 km ~ 5 Rs (Rs ~ 7.5 10^5 km) If open angle is 60 degree => shock front has an extension of 5 Rs. Particles only “see” a local shock front!

  3. Even at 1AU, particles only see “a local potion of the shock”

  4. Does a shock’s geometry change over a length scale of ~ 10 or 100 Rg? If YES, then all acceleration model need to consider ensemble average of some kind. If NO, then acceleration may only occur at parallel or perpendicular portion of a shock and acceleration may occur only when favorable condition exist, probably that is why we see large variability. What geometry is more likely to be responsible for high energy ions? Parallel or Perp?

  5. What decide the break? 0) Equal resonance condition. Li et al 2005 (parallel shock only). Break occurs at the same resonant k wave 1) Equal diffusion coefficient  condition Break occurs at the same  Cohen et al. (2003, 2005) (parallel shock and/or perp. shock ). 2) Equal acceleration time consideration Break decided by available amount of time for acceleration (parallel and/or perp. shock). The only intrinsic length scale for particle is the gyro-radius. Break occurs at the same Rg 3) Equal Rg condition? (parallel and/or perp. shock?)

  6. at and near a parallel shock ~ v3(A/Q)2 / I(k  /v) Lee (2005) If I(k) ~ k, ~ v +3 (A/Q)+2  = -1 => Bohm Approximation Q/A dependence of  • in quiet solar wind:  = (1/3) v  ,with  ~ (rg) ~(A/Q)  = 1/3 corresponding to  = -5/3 used in Li et al (2003) • at a perpendicular shock, ~ ‖1/3so ~ v (A/Q)1/9 Zank et al (2004) the generic form:  = 2,  =1 => Bohm approx.  = x,  = x-1 => parallel shock  = v (A/Q)  = 1,  =1/9 => perp. shock

  7. Case 0: resonance condition k v =  ~ Q/A ( = Q/A [eB/mp c]) Enhanced Break occurs at the same k E0 ~ v^2 ~ (Q/A)^2 I(k) Background strict (Q/A)^2 dependence k0 works for parallel shock. k

  8. Case 1: Equal diffusion coefficient Break regulated by an escape process and occurs at the SAME  Consider a parallel shock, assuming a power law turbulence:  = v (A/Q) If I(k) = k g ==> ==> E0 ~ (Q/A) 2/ Can generalize to oblique shock case, where  = || cos2()+  sin2() Cohen et al. (2003, 2005)

  9. Drury (1983) Case 2: equal acceleration time time for a particle’s momentum to increase from p to p + p.  = v (A/Q) ==> E0 ~ (Q/A) 2/ Same as case 1  = || cos2() +  sin2() Again, oblique shock

  10. Case B: parallel shock with I(k) ~ k E0 ~ (Q/A)2(+2)/(+3)  = -2 => E0 ~ (Q/A)0  = -1.5 => E0 ~ (Q/A)2/3  = 0 => E0 ~ (Q/A)4/3 breaking energy E0 for case 1&2 Case A: Bohm approx.  = 2,  =1 E0 ~ (Q/A) Seen in observation e.g. Tylka (2001) Bohm approximation may NOT be a bad approximation Case C: perpendicular shock: = 1,  =1/9 E0 ~ (Q/A)2/9 Can perp. Shock be responsible for large SEP events? Not seen yet

  11. Oblique shock?  = || cos2()+  sin2() Assume What is the Q/A dependence now? worst case scenario

  12. Case 3: Equal Rg Suppose turbulence is strong, and no wave signatures show up, then what? B ~ B Gyro-motion is not well defined! The break in this case may be decided by equaling its intrinsic length scale, Rg to some external length scale R. E = (Q/A)^2 R This becomes case zero. With a very turbulent B, no point of talking parallel or perp. B.

  13. Can E0 scale as (Q/A)2 from case 1&2? At a parallel shock if I(k) ~ k == > E0 ~ (Q/A)2(+2)/(+3) What does this mean? To have a (Q/A)2 dependence,  = . Enhanced • below a critical k, decided by the maximum proton momentum, I(k) will quickly decrease to the quiet solar wind level. I(k) Background k0 Such a sudden decrease of I(k) corresponds to  = . k

  14. clear spectral breaksin large SEP Event fluence of the Oct-Nov events R. Mewaldt et al. 2005 • spectra of large SEP events often show broken (or double) power feature. • Breaking energies seem to be ordered by (Q/M). This

  15. Spectrum form beyond the break Not necessary double power law, but if the shifting technique works, then the physical process for this part of the spectrum also has the SAME (Q/A) dependence of the break. Should examine Marty’s idea on relating E0 and the shape beyond the break.

  16. The October 29th, 2003 event • Similar spectral indices for different heavy ions • Double power law or exponential roll over spectra right after the shock This R. Mewaldt et al. 2005

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